Finite Math Examples

$w - \frac{1}{2} = - \frac{7}{5} w - \frac{5}{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $w$ and $\frac{7}{5}$ .

$w - \frac{1}{2} = - \frac{w \cdot 7}{5} - \frac{5}{2}$

Step 1.2

Move $7$ to the left of $w$ .

$w - \frac{1}{2} = - \frac{7 w}{5} - \frac{5}{2}$

Step 2

Move all terms containing $w$ to the left side of the equation.

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Step 2.1

Add $\frac{7 w}{5}$ to both sides of the equation.

$w - \frac{1}{2} + \frac{7 w}{5} = - \frac{5}{2}$

Step 2.2

To write $w$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$w \cdot \frac{5}{5} + \frac{7 w}{5} - \frac{1}{2} = - \frac{5}{2}$

Step 2.3

Combine $w$ and $\frac{5}{5}$ .

$\frac{w \cdot 5}{5} + \frac{7 w}{5} - \frac{1}{2} = - \frac{5}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{w \cdot 5 + 7 w}{5} - \frac{1}{2} = - \frac{5}{2}$

Step 2.5

Add $w \cdot 5$ and $7 w$ .

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Step 2.5.1

Reorder $w$ and $5$ .

$\frac{5 \cdot w + 7 w}{5} - \frac{1}{2} = - \frac{5}{2}$

Step 2.5.2

Add $5 \cdot w$ and $7 w$ .

$\frac{12 \cdot w}{5} - \frac{1}{2} = - \frac{5}{2}$

$\frac{12 w}{5} - \frac{1}{2} = - \frac{5}{2}$

Step 3

Move all terms not containing $w$ to the right side of the equation.

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Step 3.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{12 w}{5} = - \frac{5}{2} + \frac{1}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{12 w}{5} = \frac{- 5 + 1}{2}$

Step 3.3

Add $- 5$ and $1$ .

$\frac{12 w}{5} = \frac{- 4}{2}$

Step 3.4

Divide $- 4$ by $2$ .

$\frac{12 w}{5} = - 2$

Step 4

Multiply both sides of the equation by $\frac{5}{12}$ .

$\frac{5}{12} \cdot \frac{12 w}{5} = \frac{5}{12} \cdot - 2$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{12} \cdot \frac{12 w}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{12} \cdot \frac{12 w}{5} = \frac{5}{12} \cdot - 2$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{12} (12 w) = \frac{5}{12} \cdot - 2$

Step 5.1.1.2

Cancel the common factor of $12$ .

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Step 5.1.1.2.1

Factor $12$ out of $12 w$ .

$\frac{1}{12} (12 (w)) = \frac{5}{12} \cdot - 2$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{12} (12 w) = \frac{5}{12} \cdot - 2$

Step 5.1.1.2.3

Rewrite the expression.

$w = \frac{5}{12} \cdot - 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{12} \cdot - 2$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Factor $2$ out of $12$ .

$w = \frac{5}{2 (6)} \cdot - 2$

Step 5.2.1.1.2

Factor $2$ out of $- 2$ .

$w = \frac{5}{2 \cdot 6} \cdot (2 \cdot - 1)$

Step 5.2.1.1.3

Cancel the common factor.

$w = \frac{5}{2 \cdot 6} \cdot (2 \cdot - 1)$

Step 5.2.1.1.4

Rewrite the expression.

$w = \frac{5}{6} \cdot - 1$

Step 5.2.1.2

Combine $\frac{5}{6}$ and $- 1$ .

$w = \frac{5 \cdot - 1}{6}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $5$ by $- 1$ .

$w = \frac{- 5}{6}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$w = - \frac{5}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{5}{6}$

Decimal Form:

$w = - 0.8\overline{3}$